Minimax Simple Bayes Estimators of a Normal Variance

TL;DR

This paper establishes a closed-form minimaxity result for a class of simple Bayes estimators of a normal variance under entropy loss, building on previous work that identified their Bayesian nature.

Contribution

It provides the first closed-form proof of minimaxity for this class of estimators, confirming their optimality under entropy loss.

Findings

Proves minimaxity of the estimators in closed form

Confirms Bayesianity of the estimators

Enhances understanding of variance estimation under entropy loss

Abstract

This paper is a follow-up to Maruyama and Strawderman (2006, Journal of Statistical Planning and Inference), which identified a new class of generalized Bayes estimators with a particularly simple form for estimating a normal variance under entropy loss. Although their previous work established the Bayesianity of these estimators, it did not provide a closed-form result for their minimaxity. In this paper, we revisit the problem and establish a definitive closed-form minimaxity result for this class of simple Bayes estimators.